On hypersonic flow past of a lift airfoil (Q1062856)

The hypersonic flow at large distance from a lifting airfoil of finite dimensions is discussed based on asymptotic solutions of the Navier- Stokes equations. The medium is assumed to be a perfect gas with constant ratio of specific heats and with linear dependence of viscosity coefficients as well as thermal conductivity on the specific enthalpy. The flow field is divided into three regions, the external flow, the laminar trail and the subtrail. A cylindrical coordinate system is established and the behaviour of the flow at planes transverse to the undisturbed longitudinal flow direction is discussed. The flow field is found to be composed of different types of local vortex zones being fixed by the longitudinal component of the local vortex vector. Especially the subtrail region is shown to have the contour of an oscillating cord. The flow behaviour mainly is determined by the lift caused terms of the equations derived. From the mathematical point of view the external flow and the laminar trail are described approximately with the help of the Cauchy problem for Euler's equations. The external flow zone has the surrounding shock wave as its border. For that the Rankine-Hugoniot shock conditions are established. The special type of the shock equation as well as the equations of the velocity components used are based on descriptions which one has to take from the literature quoted. The subtrail region flow is described with the help of a self-similar variable. The approximation of the Navier-Stokes equations for this region leads to a Laplace equation type. The solutions for the different flow fields are matched with one another at their limit conditions.